Creating a Cone in 3D Euclidean Space

Creating a Cone in 3D Euclidean Space
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2015-12-14 23:02
In collections Conic Section: Parabola
This example demonstrates how to create a cone in 3D Euclidean space. It involves core mathematical concepts such as solid geometry, coordinate geometry, and trigonometry. Key construction steps use GeoGebra commands like Intersect, OrthogonalLine, Point, Cone, Sphere, Line, and Angle, with objects like A, a, B, r, b, c, d, C, e, D, E, f, g, h, F_1, i, α, text1, text3, text4, text5, text6, text7, j, k, l, m, F_2. Suitable for high school and above students learning solid geometry and coordinate geometry.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, xAxis) → A
  2. OrthogonalLine(A, xOyPlane) → a
  3. Point(a) → B
  4. Cone(A, B, r) → b, c, d
  5. Intersect(a, d, 1) → C
  6. Sphere(C, A) → e
  7. Intersect(a, e) → D, E
  8. Cone(E, B, r) → f, g, h
  9. Point(c) → F_1
  10. Line(F_1, B) → i
  11. Angle(i, a) → α